While the Soret coefficients of binary mixtures have been widely measured in the past, here we report the first measurement of the Soret coefficient of a ternary mixture in a low gravity environment on board the International Space Station. The sample was contained in a 10 mm x 10 mm x 5 mm (w, l, h) cell and was monitored by means of a Mach-Zehnder interferometer at two wavelengths. The analyzed sample was a mixture of tetrahydronaphthalene, isobutylbenzene, and dodecane at the weight fraction of 0.10.80.1. While the lateral walls of the cell did not possess complete thermal isolation, the separation of the components in the central region of the cavity was comparable to purely diffusive behavior. The same experimental parameters have been monitored in Run7 and Run12 of the Selectable Optical Diagnostics Instrument-Diffusion and Soret Coefficient experiment in order to verify the accuracy of the setup. The similarity of the results demonstrates the repeatability of thermodiffusion experiments in a microgravity environment. There was nearly equal separation of the tetrahydronaphthalene and isobutylbenzene components in opposite directions, while dodecane experienced a weak separation in the same direction as isobutylbenzene. Finally, Fourier image processing and calculations of the transient separation of the components were used to analyze the heat transfer in the system and to measure the Soret coefficients for this ternary mixture. The successful measurements shown in this work can serve as the standard for ground experiments and for numerical modeling of hydrocarbon mixtures.